Midrash Tanchuma, Vayera
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וַה' פָּקַד אֶת שָׂרָה. זֶה שֶׁאָמַר הַכָּתוּב: וְיָדְעוּ הַגּוֹיִם אֲשֶׁר יִשָּׁאֲרוּ סְבִיבוֹתֵיכֶם כִּי אֲנִי ה' בָּנִיתִי הַנֶּהֱרָסוֹת וְגוֹ' (יחזקאל לו, לו).
And the Lord remembered Sarah (Gen. 21:1). Scripture says elsewhere in allusion to this verse: Then the nations that are left round about shall know that I, the Lord, have builded the stricken places, and have planted that which was desolate: I, the Lord, have spoken it, and I will do it (Ezek. 36:36).
וְיָדְעוּ הַגּוֹיִם, אֵלּוּ הַנָּשִׁים שֶׁהָיוּ מְבַיְּשׁוֹת אֶת שָׂרָה וְקוֹרְאוֹת אוֹתָהּ עֲקָרָה. כִּי אֲנִי ה' בָּנִיתִי הַנֶּהֱרָסוֹת, שֶׁהָיְתָה נֶהֱרֶסֶת, שֶׁנֶּאֱמַר: וְאַבְרָהָם וְשָׂרָה זְקֵנִים בָּאִים בַּיָּמִים (בראשית יח, טו). נָטַעְתִּי הַנְּשַׁמָּה (יחזקאל לו, לו), שֶׁהָיְתָה אוֹמֶרֶת, אַחֲרֵי בְלֹתִי הָיְתָה לִּי עֶדְנָה. אֲנִי ה' דִּבַּרְתִּי וְעָשִׂיתִי (יחזקאל לו, לו), שֶׁנֶּאֱמַר: וַה' פָּקַד אֶת שָׂרָה כַּאֲשֶׁר אָמָר.
The nations shall know refers to the women who taunted Sarah by calling her a barren woman. I, the Lord, have builded the stricken places indicates that she was stricken with old age, as it is said: And Abraham and Sarah were old, and well stricken with age (Gen. 18:11). Have planted that which is desolate refers to her remark: After I am waxed old, shall I have pleasure? (ibid., v. 12). And I, the Lord, have spoken it, and I will do it is stated because it is said: And God remembered Sarah as He has said, and the Lord did unto Sarah as He had spoken (ibid. 21:1).
בְּרֹאשׁ הַשָּׁנָה נִפְקְדָה שָׂרָה וְנוֹלַד יִצְחָק לְשִׁבְעָה חֳדָשִׁים בְּלֵיל פֶּסַח, שֶׁנֶּאֱמַר: שׁוֹב אָשׁוּב אֵלֶיךָ כָּעֵת חַיָּה. וְאַרְבַּע עֲקָרוֹת נִפְקְדוּ בְּרֹאשׁ הַשָּׁנָה, וְאֵלּוּ הֵן: שָׂרָה וְרִבְקָה וְרָחֵל וְלֵאָה.
Sarah conceived on Rosh Hashanah, and Isaac was born in the seventh month, on the night of Passover, as is said: I will certainly return unto thee when the season cometh around (Gen. 18:10). Four barren women conceived on Rosh Hashanah: Sarah, Rebecca, Rachel, and Leah.